scholarly journals A Different Approach for Choosing a Threshold in Peaks over Threshold

2020 ◽  
Vol 9 (4) ◽  
pp. 838-848
Author(s):  
Andrehette Verster ◽  
Lizanne Raubenheimer
Keyword(s):  
Bayesian Approach ◽  
Posterior Distribution ◽  
Visual Inspection ◽  
Extreme Value ◽  
Optimal Threshold ◽  
Extreme Value Index ◽  
Threshold Values ◽  
Peaks Over Threshold ◽  
Generalized Model

In Extreme Value methodology the choice of threshold plays an important role in efficient modelling of observations exceeding the threshold. The threshold must be chosen high enough to ensure an unbiased extreme value index but choosing the threshold too high results in uncontrolled variances. This paper investigates a generalized model that can assist in the choice of optimal threshold values in the γ positive domain. A Bayesian approach is considered by deriving a posterior distribution for the unknown generalized parameter. Using the properties of the posterior distribution allows for a method to choose an optimal threshold without visual inspection.

scholarly journals A Double-indexed Functional Hill Process and Applications

2016 ◽  
Vol 8 (4) ◽  
pp. 144
Author(s):  
Modou Ngom ◽  
Gane Samb Lo
Keyword(s):  
Stochastic Process ◽  
Distribution Function ◽  
Asymptotic Behaviour ◽  
Stochastic Processes ◽  
Order Statistics ◽  
Finite Dimension ◽  
Domain Of Attraction ◽  
Extreme Value ◽  
Extreme Value Index

<div>Let $X_{1,n} \leq .... \leq X_{n,n}$ be the order statistics associated with a sample $X_{1}, ...., X_{n}$ whose pertaining distribution function (\textit{df}) is $F$. We are concerned with the functional asymptotic behaviour of the sequence of stochastic processes</div><div> </div><div>\begin{equation}<br />T_{n}(f,s)=\sum_{j=1}^{j=k}f(j)\left( \log X_{n-j+1,n}-\log<br />X_{n-j,n}\right)^{s} ,  \label{fme}<br />\end{equation}</div><div> </div><div>indexed by some classes $\mathcal{F}$ of functions $f:\mathbb{N}%^{\ast}\longmapsto \mathbb{R}_{+}$ and $s \in ]0,+\infty[$ and where $k=k(n)$ satisfies</div><div> </div><div>\begin{equation*}<br />1\leq k\leq n,k/n\rightarrow 0\text{ as }n\rightarrow \infty .<br />\end{equation*}</div><div> </div><div>We show that this is a stochastic process whose margins generate estimators of the extreme value index when $F$ is in the extreme domain of attraction. We focus in this paper on its finite-dimension asymptotic law and provide a class of new estimators of the extreme value index whose performances are compared to analogous ones. The results are next particularized for one explicit class $\mathcal{F}$.</div>

scholarly journals A Bayesian approach to the identification of panmictic populations and the assignment of individuals

2001 ◽  
Vol 78 (1) ◽  
pp. 59-77 ◽  
Author(s):  
KEVIN J. DAWSON ◽  
KHALID BELKHIR
Keyword(s):  
Bayesian Approach ◽  
Posterior Distribution ◽  
Clustering Algorithm ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Marker Loci ◽  
Hierarchical Clustering Algorithm ◽  
Source Populations ◽  
Low Dimensional ◽  
Number Of Individuals

We present likelihood-based methods for assigning the individuals in a sample to source populations, on the basis of their genotypes at co-dominant marker loci. The source populations are assumed to be at Hardy–Weinberg and linkage equilibrium, but the allelic composition of these source populations and even the number of source populations represented in the sample are treated as uncertain. The parameter of interest is the partition of the set of sampled individuals, induced by the assignment of individuals to source populations. We present a maximum likelihood method, and then a more powerful Bayesian approach for estimating this sample partition. In general, it will not be feasible to evaluate the evidence supporting each possible partition of the sample. Furthermore, when the number of individuals in the sample is large, it may not even be feasible to evaluate the evidence supporting, individually, each of the most plausible partitions because there may be many individuals which are difficult to assign. To overcome these problems, we use low-dimensional marginals (the ‘co-assignment probabilities’) of the posterior distribution of the sample partition as measures of ‘similarity’, and then apply a hierarchical clustering algorithm to identify clusters of individuals whose assignment together is well supported by the posterior distribution. A binary tree provides a visual representation of how well the posterior distribution supports each cluster in the hierarchy. These methods are applicable to other problems where the parameter of interest is a partition of a set. Because the co-assignment probabilities are independent of the arbitrary labelling of source populations, we avoid the label-switching problem of previous Bayesian methods.

Bayesian approach and extreme value theory in economic analysis of forestry projects

2019 ◽  
Vol 105 ◽  
pp. 64-71 ◽  
Author(s):  
Thiago Taglialegna Salles ◽  
Denismar Alves Nogueira ◽  
Luiz Alberto Beijo ◽  
Liniker Fernandes da Silva
Keyword(s):  
Economic Analysis ◽  
Bayesian Approach ◽  
Extreme Value Theory ◽  
Value Theory ◽  
Extreme Value

scholarly journals Claims Reserving in Continuous Time; A Nonparametric Bayesian Approach

1996 ◽  
Vol 26 (2) ◽  
pp. 139-164 ◽  
Author(s):  
Svend Haastrup ◽  
Elja Arjas
Keyword(s):  
Bayesian Approach ◽  
Posterior Distribution ◽  
Continuous Time ◽  
Marked Point ◽  
Marked Point Process ◽  
Nonparametric Bayesian ◽  
Occurrence Time ◽  
One Dimensional ◽  
The Individual ◽  
Reporting Delay

AbstractOccurrences and developments of claims are modelled as a marked point process. The individual claim consists of an occurrence time, two covariates, a reporting delay, and a process describing partial payments and settlement of the claim. Under certain likelihood assumptions the distribution of the process is described by 14 one-dimensional components. The modelling is nonparametric Bayesian. The posterior distribution of the components and the posterior distribution of the outstanding IBNR and RBNS liabilities are found simultaneously. The method is applied to a portfolio of accident insurances.

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